On n-Coherent Rings and (n, d)-Injective Modules

• 作者: Baiyu Ouyang Dongdong Zhang
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 凝聚环 环和 模块 非负整数 证明 MR RM 权利
• 年，卷（期）: 2015,（2）
• 页码范围: 349-360
• 页数: 12页
• 分类号: O153.3
• 语种: 中文

摘要

Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of (n, d)- injective left R-modules, and Fn,d the class of (n, d)-flat right R-modules. In this paper, we prove that if R is a left n-coherent ring and m ≥ 2, then gl-right-Jn,a-dimRM ≤ m if and only if gl-left-Jn,d-dimRM ≤ m -- 2, if and only if Extm+k(M, N) = 0 for all left R-modules M, N and all k 〉 -1, if and only if Extm-l(M, N) = 0 for all left R-modules M, N. Meanwhile, we prove that if R is a left n-coherent ring, then - - is right balanced on MR *RM by Fn,d * Jn,d, and investigate the global right Jn,d-dimension of RM and the global right Fn,d-dimension of MR by right derived functors of - -. Some known results are obtained as corollaries.